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非线性互补问题的组合同伦算法
引用本文:王秀玉,姜兴武,刘庆怀.非线性互补问题的组合同伦算法[J].应用数学学报,2012,35(3):430-440.
作者姓名:王秀玉  姜兴武  刘庆怀
作者单位:1. 长春工业大学基础科学学院,长春,130012
2. 吉林工商学院基础部,长春,130062
3. 长春工业大学应用数学所,长春,130012
基金项目:国家自然科学基金,吉林省自然科学基金
摘    要:针对拟P_*-映射和P(τ,α,β)-映射所对应的非线性互补问题,本文对其解的存在性及有效求解算法进行了研究.文中利用组合同伦方法给出了这两类非线性互补问题存在有界解的构造性证明,并利用预估校正方法对同伦路径进行跟踪,得到了互补问题的解.通过数值算例验证了该算法的有效性.

关 键 词:互补问题  同伦算法  拟P_*-映射  P(τ  α  β)-映射

The Combined Homotopy Method for Nonlinear Complementarity Problems
WANG XIUYU , JIANG XINGWU , LIU QINGHUAI.The Combined Homotopy Method for Nonlinear Complementarity Problems[J].Acta Mathematicae Applicatae Sinica,2012,35(3):430-440.
Authors:WANG XIUYU  JIANG XINGWU  LIU QINGHUAI
Institution:(Institute of Applied Mathematics,Changchun University of Technology,Changchun 130012)
Abstract:For the nonlinear complementarity problems with P~*-mapping and P(τ,α,β)-mapping, we study the existence and effective algorithm of a solution.We give the constructive proof of existence of a bounded solution by the homotopy method for this two classes of complementarity problem,and trace the homotopy path by using the predictor-corrector method,obtain a solution of the nonlinear complementarity problems.Numerical examples are presented to show the effectiveness of the algorithm.
Keywords:complementarity problem  homotopy method  quasi-P~*-mapping  P(τ  α  β)- mapping
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